13 research outputs found
Resolving Over-constrained Probabilistic Temporal Problems through Chance Constraint Relaxation
When scheduling tasks for field-deployable systems, our solutions must be robust to the uncertainty inherent in the real world. Although human intuition is trusted to balance reward and risk, humans perform poorly in risk assessment at the scale and complexity of real world problems. In this paper, we present a decision aid system that helps human operators diagnose the source of risk and manage uncertainty in temporal problems. The core of the system is a conflict-directed relaxation algorithm, called Conflict-Directed Chance-constraint Relaxation (CDCR), which specializes in resolving over-constrained temporal problems with probabilistic durations and a chance constraint bounding the risk of failure. Given a temporal problem with uncertain duration, CDCR proposes execution strategies that operate at acceptable risk levels and pinpoints the source of risk. If no such strategy can be found that meets the chance constraint, it can help humans to repair the over-constrained problem by trading off between desirability of solution and acceptable risk levels. The decision aid has been incorporated in a mission advisory system for assisting oceanographers to schedule activities in deep-sea expeditions, and demonstrated its effectiveness in scenarios with realistic uncertaintyBoeing Company (Grant MIT-BA-GTA-1
Chance-Constrained Probabilistic Simple Temporal Problems
Scheduling under uncertainty is essential to many autonomous systems and logistics tasks. Probabilistic methods for solving temporal problems exist which quantify and attempt to minimize the probability of schedule failure. These methods are overly conservative, resulting in a loss in schedule utility. Chance constrained formalism address over-conservatism by imposing bounds on risk, while maximizing utility subject to these risk bounds. In this paper we present the probabilistic Simple Temporal Network (pSTN), a probabilistic formalism for representing temporal problems with bounded risk and a utility over event timing. We introduce a constrained optimisation algorithm for pSTNs that achieves compactness and efficiency through a problem encoding in terms of a parameterised STNU and its reformulation as a parameterised STN. We demonstrate through a car sharing application that our chance-constrained approach runs in the same time as the previous probabilistic approach, yields solutions with utility improvements of at least 5% over previous arts, while guaranteeing operation within the specified risk bound.National Science Foundation (U.S.) (Grant No. IIS-1017992
Chance-constrained Scheduling via Conflict-directed Risk Allocation
Temporal uncertainty in large-scale logistics forces one to trade off between lost efficiency through built-in slack and costly replanning when deadlines are missed. Due to the difficulty of reasoning about such likelihoods and consequences, a computational framework is needed to quantify and bound the risk of violating scheduling requirements. This work addresses the chance-constrained scheduling problem, where actions’ durations are modeled probabilistically. Our solution method uses conflict-directed risk allocation to efficiently compute a scheduling policy. The key insight, compared to previous work in probabilistic scheduling, is to decouple the reasoning about temporal and risk constraints. This decomposes the problem into a separate master and subproblem, which can be iteratively solved much quicker. Through a set of simulated car-sharing scenarios, it is empirically shown that conflict-directed risk allocation computes solutions nearly an order of magnitude faster than prior art does, which considers all constraints in a single lump-sum optimization
On Expected Value Strong Controllability
The Probabilistic Simple Temporal Network (PSTN) generalizes Simple Temporal Networks with Uncertainty (STNUs) by introducing probability distributions over the timing of uncontrollable timepoints. PSTNs are controllable if there is a strategy to execute the controllable timepoints while bounding the risk of violating any constraint to a small value. If this risk bound can't be satisfied, PSTNs are not considered controllable. We introduce the Expected Value Probabilistic SimpleTemporal Network (EPSTN), which extends PSTNs by including a benefit to the satisfaction of temporal constraints. We study the problem of Expected Value Strong Controllability (EvSC) of EPSTNs, which seeks a schedule maximizing the expected value of satisfied constraints. We solve the EvSC problem by extending a previously developed linear program, combined with search over constraints to violate at execution time. We describe conditions under which the solution to this linear program is the maximum expected value schedule. We then show how to search for constraints to discard, using the linear program at the core of the search. While the general problem is shown to be exponential, we conclude by providing several methods to bound the complexity of search
Reasoning and querying bounds on differences with layered preferences
Artificial intelligence largely relies on bounds on differences (BoDs) to model binary constraints regarding different dimensions, such as time, space, costs, and
calories. Recently, some approaches have extended the
BoDs framework in a fuzzy, \u201cnoncrisp\u201d direction,
considering probabilities or preferences. While previous
approaches have mainly aimed at providing an
optimal solution to the set of constraints, we propose
an innovative class of approaches in which constraint
propagation algorithms aim at identifying the \u201cspace of
solutions\u201d (i.e., the minimal network) with their preferences,
and query answering mechanisms are provided
to explore the space of solutions as required, for
example, in decision support tasks. Aiming at generality,
we propose a class of approaches parametrized
over user\u2010defined scales of qualitative preferences (e.g.,
Low, Medium, High, and Very High), utilizing the resume
and extension operations to combine preferences,
and considering different formalisms to associate preferences
with BoDs. We consider both \u201cgeneral\u201d preferences
and a form of layered preferences that we call
\u201cpyramid\u201d preferences. The properties of the class of
approaches are also analyzed. In particular, we show
that, when the resume and extension operations are
defined such that they constitute a closed semiring, a
more efficient constraint propagation algorithm can be used. Finally, we provide a preliminary implementation
of the constraint propagation algorithms
Proactive Algorithms for Job Shop Scheduling with Probabilistic Durations
Most classical scheduling formulations assume a fixed and known duration for
each activity. In this paper, we weaken this assumption, requiring instead that
each duration can be represented by an independent random variable with a known
mean and variance. The best solutions are ones which have a high probability of
achieving a good makespan. We first create a theoretical framework, formally
showing how Monte Carlo simulation can be combined with deterministic
scheduling algorithms to solve this problem. We propose an associated
deterministic scheduling problem whose solution is proved, under certain
conditions, to be a lower bound for the probabilistic problem. We then propose
and investigate a number of techniques for solving such problems based on
combinations of Monte Carlo simulation, solutions to the associated
deterministic problem, and either constraint programming or tabu search. Our
empirical results demonstrate that a combination of the use of the associated
deterministic problem and Monte Carlo simulation results in algorithms that
scale best both in terms of problem size and uncertainty. Further experiments
point to the correlation between the quality of the deterministic solution and
the quality of the probabilistic solution as a major factor responsible for
this success
Risk allocation for temporal risk assessment
Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 63-64).Temporal uncertainty arises when performing any activity in the natural world. When activities are composed into temporal plans, then, there is a risk of not meeting the plan requirements. Currently, we do not have quantitatively precise methods for assessing temporal risk of a plan. Existing methods that deal with temporal uncertainty either forgo probabilistic models or try to optimize a single objective, rather than satisfy multiple objectives. This thesis offers a method for evaluating whether a schedule exists that meets a set of temporal constraints, with acceptable risk of failure. Our key insight is to assume a form of risk allocation to each source of temporal uncertainty in our plan, such that we may reformulate the probabilistic plan into an STNU parameterized on the risk allocation. We show that the problem becomes a deterministic one of finding a risk allocation which implies a schedulable STNU within acceptable risk. By leveraging the principles behind STNU analysis, we derive conditions which encode this problem as a convex feasibility program over risk allocations. Furthermore, these conditions may be learned incrementally as temporal conflicts. Thus, to boost computational efficiency, we employ a generate-and-test approach to determine whether a schedule may be found.by Andrew J. Wang.M. Eng
Optimising Flexibility of Temporal Problems with Uncertainty
Temporal networks have been applied in many autonomous systems.
In real situations, we cannot ignore the uncertain factors when
using those autonomous systems. Achieving robust schedules and
temporal plans by optimising flexibility to tackle the
uncertainty is the motivation of the thesis.
This thesis focuses on the optimisation problems of temporal
networks with uncertainty and controllable options in the field
of Artificial Intelligence Planning and Scheduling. The goal of
this thesis is to construct flexibility and robustness metrics
for temporal networks under the constraints of different levels
of controllability. Furthermore, optimising flexibility for
temporal plans and schedules to achieve robust solutions with
flexible executions.
When solving temporal problems with uncertainty, postponing
decisions according to the observations of uncertain events
enables flexible strategies as the solutions instead of fixed
schedules or plans. Among the three levels of controllability of
the Simple Temporal Problem with Uncertainty (STPU), a problem is
dynamically controllable if there is a successful dynamic
strategy such that every decision in it is made according to the
observations of past events.
In the thesis, we make the following contributions. (1) We
introduce an optimisation model for STPU based on the existing
dynamic controllability checking algorithms. Some flexibility and
robustness measures are introduced based on the model. (2) We
extend the definition and verification algorithm of dynamic
controllability to temporal problems with controllable discrete
variables and uncertainty, which is called Controllable
Conditional Temporal Problems with Uncertainty (CCTPU). An
entirely dynamically controllable strategy of CCTPU consists of
both temporal scheduling and variable assignments being
dynamically decided, which maximize the flexibility of the
execution. (3) We introduce optimisation models of CCTPU under
fully dynamic controllability. The optimisation models aim to
answer the questions how flexible, robust or controllable a
schedule or temporal plan is. The experiments show that making
decisions dynamically can achieve better objective values than
doing statically.
The thesis also contributes to the field of AI planning and
scheduling by introducing robustness metrics of temporal
networks, proposing an envelope-based algorithm that can check
dynamic controllability of temporal networks with uncertainty and
controllable discrete decisions, evaluating improvements from
making decisions strongly controllable to temporally dynamically
controllable and fully dynamically controllable and comparing the
runtime of different implementations to present the scalability
of dynamically controllable strategies